In one embodiment, L dimensional images are trained, mapped, and aligned to an M dimensional topology to obtain azimuthal angles. The aligned L dimensional images are then trained and mapped to an N dimensional topology to obtain 2N vertex classifications. The azimuthal angles and the 2N vertex classifications are used to map L dimensional images into O dimensional images.
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1. A method for aligning and classifying images, comprising: providing stored 2-dimensional image data to a computer processor as a set of input 2-dimensional images; training, mapping, and aligning the 2-dimensional images to a 3-dimensional cylindrical topology to obtain azimuthal angles with respect to the 2-dimensional images; training and mapping the aligned 2-dimensional images to an N-dimensional topology to obtain a set of 2 N vertex classifications; and mapping the 2-dimensional images to M-dimensional constructs based upon the set of 2 N vertex classifications and the azimuthal angles.
The invention is a method for aligning and classifying images using a computer. It takes 2D images, maps them onto a 3D cylindrical shape to calculate azimuthal angles (rotational positions). Then, it uses these aligned 2D images and maps them to a higher-dimensional space (N-dimensional) to group them into 2 to the power of N vertex classifications. Finally, it maps the original 2D images into a new M-dimensional representation based on both the azimuthal angles and the vertex classifications. This creates a new way to represent the original image data.
2. The method of claim 1 , further comprising repeating the training, mapping and aligning step using a class of images associated with at least one vertex classification of the 2 N vertex classifications, and obtained from the training and mapping step, thereby hyperaligning the aligned 2-dimensional images.
The image alignment and classification method, which takes 2D images, maps them onto a 3D cylindrical shape to calculate azimuthal angles, maps the aligned images to an N-dimensional space for vertex classifications, and then maps the 2D images into an M-dimensional representation, can be improved by repeating the initial training, mapping, and alignment step. This repetition uses a subset of images that belong to a specific vertex classification identified in the previous mapping step. This "hyperalignment" process further refines the alignment of the 2D images.
3. The method of claim 1 wherein the 3-dimensional cylindrical topology comprises a cylinder having a circumference and a height defining a circumference to height ratio, the circumference to height ratio being initially determined based on an initial small circumference, and further comprising scaling up the circumference while maintaining the circumference to height ratio as constant, whereby the azimuthal angles are obtained at higher resolution.
In the image alignment and classification method where 2D images are mapped to a 3D cylindrical shape to get azimuthal angles, the cylindrical shape's proportions are important. The cylinder has a circumference and a height, creating a ratio. Initially, the circumference is small. The method scales up the circumference while keeping the circumference-to-height ratio constant. This scaling improves the resolution of the azimuthal angles, allowing for finer-grained rotational positioning of the images.
4. The method of claim 1 , wherein the step of training, mapping, and aligning the 2-dimensional images includes performing the training based upon a similarity between 2-dimensional prototype images and the 2-dimensional images.
In the image alignment and classification method where 2D images are mapped to a 3D cylindrical shape to get azimuthal angles, the training and mapping process involves comparing the input 2D images to a set of 2D prototype images. The training is based on how similar the input images are to these prototypes. This similarity-based training helps to accurately map and align the images on the cylindrical topology.
5. The method of claim 1 , further comprising determining if the azimuthal angles are correct based upon checking if the azimuthal angles reside within a predetermined range of standard deviations that is acceptable for a desired precision.
The image alignment and classification method, which involves calculating azimuthal angles, includes a verification step. After calculating the azimuthal angles, the method checks if these angles are within a predefined range of acceptable standard deviations. This check ensures that the angles are accurate enough for the desired level of precision in image alignment and classification.
6. The method of claim 1 , wherein the aligning of the 2-dimensional images is based on a random rotation of input images.
In the image alignment and classification method, the step where 2D images are aligned, this alignment is achieved through a random rotation of the input images. The method randomly rotates the input images as part of the process of mapping and aligning them onto the 3D cylindrical shape. This random rotation helps in achieving a better overall alignment of the image data.
7. The method of claim 1 , wherein the step of training and mapping the aligned 2-dimensional images in a N-dimensional topology to obtain 2 N vertex classifications further comprises: inputting, to the processing computer, N dimensions of a hyper parallelepiped, training cycles, initial learning rate, and initial learning radius of the hyper parallelepiped, and determining 2 N vertex classifications within the N-dimensional parallelepiped.
In the image alignment and classification method, after mapping the 2D images to a 3D cylinder, the next step is to train and map the aligned images into an N-dimensional space to obtain 2 to the power of N vertex classifications. This involves providing the computer with parameters such as the dimensions of a hyper-parallelepiped (N dimensions), the number of training cycles, an initial learning rate, and an initial learning radius for the hyper-parallelepiped. The system then determines the 2 to the power of N vertex classifications within this N-dimensional space based on these parameters.
8. The method of claim 7 wherein the initial learning rate is set at a value so that a predetermined number of input aligned 2-dimensional images are substantially free of a biasing effect on training.
In the image alignment and classification method with N-dimensional vertex classification, to determine 2 to the power of N vertex classifications within the N-dimensional parallelepiped, the initial learning rate is set to a specific value. This value ensures that a certain number of input aligned 2D images are not significantly biased during the training process. This prevents individual images from unduly influencing the overall classification results, ensuring a more balanced and accurate training outcome.
9. The method of claim 1 , wherein the cylindrical topology consists of an array of prototype images that tile a surface of the topology in a rectangular array or rows and columns, the prototype images initially comprising random pixel values and morphing in each iteration of the step of training in appearance toward an appearance of one of an input 2-dimensional training image for each step of training.
In the image alignment and classification method using a 3D cylindrical topology, this topology is represented by an array of prototype images that cover the surface of the cylinder in rows and columns. Initially, these prototype images have random pixel values. During each training iteration, the pixel values of the prototype images are modified to resemble one of the input 2D training images. This iterative morphing process allows the prototype images to adapt and better represent the features of the input images.
10. The method of claim 9 further comprising selecting a most similar prototype image from the prior step of morphing and thereafter morphing other images based upon the most similar image.
The image alignment and classification method, which uses prototype images on a cylindrical surface that morph towards input images, further refines this process. After each morphing step, the method selects the prototype image that is most similar to one of the input images. Subsequently, it uses this "most similar" prototype as a basis for morphing other prototype images on the cylindrical surface. This accelerates and focuses the training process.
11. The method of claim 10 wherein images located at a closer distance to the most similar image on a surface of the cylindrical topology are morphed to a greater extent than images located at a greater distance.
In the image alignment and classification method, using prototype images on the cylindrical surface and a "most similar" image, the morphing process is distance-dependent. Prototype images that are located closer to the "most similar" prototype image on the surface of the cylindrical topology are morphed to a greater extent. Conversely, prototype images that are farther away are morphed to a lesser extent. This localized morphing ensures that the topology adapts more precisely to the input images.
12. The method of claim 1 , wherein the step of training, mapping and aligning 2-dimensional images onto the 3-dimensional cylindrical topology further comprises: inputting the 2-dimensional images to the computer processor; inputting metrics to the computer processor, the metrics including a circumference to height ratio of the cylindrical topology, a specific circumference based on a desired resolution of the azimuthal angles, an initial learning rate, number of training cycles, and an initial learning radius; determining symmetry of the 2-dimensional images and an identity of the azimuthal angles based on the input information; and rotationally aligning the input 2-dimensional images by applying the azimuthal angles to the input 2-dimensional images.
In the image alignment and classification method where 2D images are mapped onto a 3D cylinder, this mapping process involves: inputting the 2D images to the computer, inputting metrics (circumference-to-height ratio of the cylinder, a circumference based on desired azimuthal angle resolution, initial learning rate, training cycles, and initial learning radius), determining symmetry of the 2D images and identity of azimuthal angles based on the input information, and rotationally aligning the input 2D images by applying the azimuthal angles.
13. The method of claim 12 , wherein the step of determining symmetry further comprises reviewing the mapped 2-dimensional images to determine a degree of rotation and direction of rotation of the mapped 2-dimensional images with respect to the circumference of the 3-dimensional cylindrical topology.
In the image alignment and classification method, in the step of mapping 2D images to a 3D cylinder using parameters and then determining symmetry, determining symmetry includes reviewing the mapped 2D images to determine the degree of rotation and direction of rotation of the mapped 2D images with respect to the circumference of the 3D cylindrical topology. This assesses how much each image needs to be rotated, and in which direction, to achieve proper alignment on the cylinder.
14. The method of claim 12 , further comprising repeating the step of inputting the aligned 2-dimensional images to determine the relative precision of the azimuthal angles, wherein the determination is based upon how tightly constrained the azimuthal angles are when the corresponding aligned 2-dimensional images are mapped to the 3-dimensional cylindrical topology.
The image alignment and classification method which maps 2D images to a 3D cylinder using parameters, determines symmetry and rotationally aligns images, further comprises repeating the step of inputting the aligned 2D images to determine the relative precision of the azimuthal angles. This determination is based upon how tightly constrained the azimuthal angles are when the corresponding aligned 2D images are mapped to the 3D cylindrical topology. Essentially, the system checks how consistent the azimuthal angles are after alignment.
15. The method of claim 2 , wherein the step of hyperaligning is repeated until a predetermined degree of precision is obtained for the azimuth angles by repeating the training and mapping step to obtain a new set of 2 N vertex classifications followed by performing the training, mapping and aligning step, using another class of images associated with at least one vertex classification of the new set of 2 N vertex classifications.
In the refined image alignment and classification method, the hyperalignment step (repeating training, mapping, and aligning with a subset of images from a specific vertex classification, from the method comprising of taking 2D images, mapping them onto a 3D cylindrical shape to calculate azimuthal angles, mapping the aligned images to an N-dimensional space for vertex classifications, and then mapping the 2D images into an M-dimensional representation) is repeated until a predetermined degree of precision is achieved for the azimuthal angles. This involves obtaining a new set of 2 to the power of N vertex classifications, and then repeating the training, mapping, and aligning step, using another class of images associated with at least one vertex classification of the new set.
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May 6, 2005
August 6, 2013
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